The Murder in the Cathedral is about a martyrdom that occurred in 1170. Does it still have meaning for a contemporary audience?
Absolutely! This play is not just about the killing of Thomas a Becket, it is about standing up for what is right in the face of unpopularity. Henry wanted Thomas to allow him to use his friendship and his church title to abuse the power of the church for Henry's benefit. Thomas would not allow this abuse of power to happen--a very honorable and courageous display of not giving into peer pressure.
Who among us is not faced with that on a daily basis? We need not fool ourselves into thinking that someone as powerful as Henry II is breathing down our necks, but we do face these challenges--gossip at the office or nip it in the bud? Go with friends to a New Year's Eve party and drive home inibriated or stand up for the right thing to do and call a non-impaired friend/family member to come pick us up? Do drugs to fit in, or "Just Say 'No'" and risk being unpopular? Join a gang or dare to remain independent? Show my intelligence at school or be "cool" and act dumb?
The power struggle may not be the same, but the issues are very real and extremely relevant to today's world.
Murder in the Cathedral is not so much a story of a martrydom as it is the story of a political assassination; therefore, it is relevant for today and the future. Henry II of England wanted state law to supersede church law, but Thomas Becket firmly opposed him. The three knights who killed Becket, therefore, were trying to please their king by removing a political opponent. They never intended to create a martyr.
History is full of examples of such political assassinations. The murders of Archduke Ferdinand before WWI, the killing of Gandhi, and even the assassination of John F. Kennedy are such examples. My answer to your question is yes, this story is still relevant for today.